Students’ emerging algebraic thinking in the middle school years

There is a strong case for arguing that the application of relational thinking to solve number sentences embodies features of mathematical thinking that are centrally important to algebra. This study investigates how well students in Years 5, 6, and 7 in three countries were able to use relational thinking to solve different types of number sentences. There were other students who appeared to rely solely on computational method to solve the same number sentences. The study then examined whether those who had shown clear evidence of relational strategies to solve the number sentences were better placed to solve symbolic sentences than those who had used only computational methods on these number sentences. Relational Thinking In their study, “The algebraic nature of students ’ numerical manipulation in the New Zealand Numeracy Project”, Irwin and Britt (2005) argue that the methods of compensating and equivalence that some students use in solving number sentences may provide a foundation for algebraic thinking (p. 169). These authors give as an example the number sentence 47 + 25 which can be transformed into 50 + 22 by “adding 3 ” to 47 and “subtracting 3 ” from 25. They claim (p. 171) “that when students apply this strategy t